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, 38 (2), 221-34

Dendritic Morphology Predicts Pattern Recognition Performance in Multi-Compartmental Model Neurons With and Without Active Conductances

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Dendritic Morphology Predicts Pattern Recognition Performance in Multi-Compartmental Model Neurons With and Without Active Conductances

Giseli de Sousa et al. J Comput Neurosci.

Abstract

In this paper we examine how a neuron's dendritic morphology can affect its pattern recognition performance. We use two different algorithms to systematically explore the space of dendritic morphologies: an algorithm that generates all possible dendritic trees with 22 terminal points, and one that creates representative samples of trees with 128 terminal points. Based on these trees, we construct multi-compartmental models. To assess the performance of the resulting neuronal models, we quantify their ability to discriminate learnt and novel input patterns. We find that the dendritic morphology does have a considerable effect on pattern recognition performance and that the neuronal performance is inversely correlated with the mean depth of the dendritic tree. The results also reveal that the asymmetry index of the dendritic tree does not correlate with the performance for the full range of tree morphologies. The performance of neurons with dendritic tapering is best predicted by the mean and variance of the electrotonic distance of their synapses to the soma. All relationships found for passive neuron models also hold, even in more accentuated form, for neurons with active membranes.

Figures

Fig. 1
Fig. 1
Samples of tree morphologies with 22 terminal points generated by an exhaustive tree-generation algorithm. The values shown indicate asymmetry index (top) and mean depth (bottom). For these neurons, all compartments were 10 μm long
Fig. 2
Fig. 2
Six sample trees with 128 terminal points generated by the selective tree-generation algorithm. The values indicate the tree asymmetry index (top) and the mean depth (bottom). The trees are visualised using the NEURON simulator tool (Hines and Carnevale 1997), which displays the long dendritic shafts of the most asymmetric trees as a circle. Note that the angles between branches are used only for visualisation and do not affect the neuron’s electrotonic properties. Depending on the simulation (as explained in the Methods), all compartments are either 5 μm or 10 μm long
Fig. 3
Fig. 3
Mapping input pattern to trees. The diagram shows how the same input pattern is mapped to each synapse in the most symmetric and the most asymmetric morphologies
Fig. 4
Fig. 4
Pattern recognition in the passive neuron model. The voltage traces (left) show the EPSP responses at the soma to 10 stored patterns (blue traces) and 10 novel patterns (red traces). The histogram shows the frequency of the EPSP peak responses for both stored and novel patterns (bin-width 1 mV). The resulting signal-to-noise ratio is 23.76
Fig. 5
Fig. 5
Pattern recognition in the active model. The neuronal response in active neuronal models was determined by counting the number of spikes after pattern presentation. Two examples of neuronal response are shown in (a), for novel and stored patterns. The raster plot in (b) represents the responses to 10 stored patterns (blue dots) and 10 novel patterns (red dots). The histogram in (c) shows the frequency of the number of spikes produced for stored and novel patterns. The resulting signal-to-noise ratio is 16.20. Scale bars: 5 ms, 20 mV
Fig. 6
Fig. 6
The performance of every binary tree with 22 terminal points is plotted against asymmetry index (a) and mean depth (b). For each metric, a different bin width is used to result in a similar resolution of data (0.01 for asymmetry index and 0.1 for mean depth respectively). The pattern recognition performance was calculated by averaging over the s/n ratio in response to five different sets of patterns presented to each neuronal morphology. Error bars represent the standard deviation calculated across all trees within the bin
Fig. 7
Fig. 7
Pattern recognition performance of passive neurons having dendrites selectively generated from the space of trees with 128 terminal points. The scatter plot in (a) shows, for each of 155,000 trees, the signal-to-noise ratios assessed over five trials of a 20-pattern recognition task (blue data points). For the construction of the red curve, one tree was randomly selected from each bin, and its performance re-calculated over 100 trials of the pattern recognition task. (b) plots the mean (calculated from data points in (a)) and standard deviation of the signal-to-noise ratio over all trees within the same bin (bin-width 0.01) against the asymmetry index. (c) shows the signal-to-noise ratio of all trees within the same bin (bin-width 1) against the mean depth of these trees
Fig. 8
Fig. 8
Pattern recognition performance of active (red) and passive (blue) neuronal models with selectively generated dendritic morphologies drawn from the space of trees with 128 terminal points. Results were obtained by generating a population of 155,000 trees spanning the full range of each metric, from which five trees were randomly selected in each bin, using bin-widths of 0.05 for the asymmetry index (a) and 2.5 for the mean depth (b). Each data point and error bar plots the average and standard deviation over the five selected neurons, each tested over 100 trials in a 20-pattern recognition task. Note that in these simulations, as explained in Section 2.4, the passive neurons received the same afferent spike trains and background noise as used for the active neurons
Fig. 9
Fig. 9
Asymmetry index against mean depth for selectively generated trees with 128 terminal points. The plot shows that all trees with asymmetry index up to 0.4 have a similar low mean depth. The inset in the top left corner shows example trees with the same mean depth (8.15) but different asymmetry indices (presented below each tree). The bottom left inset highlights the trees with asymmetry index between 0 and 0.3, which all have a mean depth around 7.2. The bin width used for the asymmetry index is 0.02
Fig. 10
Fig. 10
Robustness of the pattern recognition performance in passive neurons with 128 terminal points. Results were obtained by averaging the pattern recognition task over 100 trials for each of the 100 samples of morphologies used in Figure 7a. The green data points in each panel represent the control simulation, where the parameters used were the same as in Figure 7. Panel (a) shows that the pattern recognition task is robust to varying amounts of background noise. In (b), we demonstrate that the pattern recognition performance was affected by increasing the number of stored patterns presented to the model, but the overall pattern of performance against mean depth persists. Panel (c) shows that the results are robust when the sparsity varied. Panel (d) shows that the ratio of NMDA and AMPA receptors affects pattern recognition performance, whilst preserving the inverse correlation between performance and mean depth. The NMDA receptors were modelled as described in Graham (2001)
Fig. 11
Fig. 11
Pattern recognition performance of model neurons in the presence of dendritic tapering. The tapering factor was varied from 0.7 to 1. The morphological metrics used, asymmetry index (a), mean depth (b), and mean and variance of electrotonic path length (c, d) are plotted on a logarithmic scale for visualisation purposes. The signal-to-noise ratio was calculated by averaging over 100 trials of 20 patterns
Fig. 12
Fig. 12
Comparison of pattern recognition in neurons with the most symmetric and the most asymmetric dendritic morphologies. The s/n ratios, shown on the top of each histogram, are calculated using the EPSP peaks resulting from the presentation of sets of stored (blue) and novel (red) patterns. On top of each of the EPSP traces the neuronal morphologies used in this experiment are shown, with blue dots that represent the location of each active synapse for the lowest and highest response obtained for stored patterns. The yellow circles shown for the asymmetric morphology indicate the location of clusters of active synapses that are located predominantly at the distal or proximal end of the dendrite, leading to the lowest or highest response, respectively. The spatial distributions of active synapses for the stored patterns (bottom graphs, x-axis in μm) also explain why the performance is better for the most symmetric morphology (right), as this morphology has a larger number of active synapses closer to the soma and consequently, a smaller variance of synaptic distances and somatic voltage responses when compared to the most asymmetric morphology (left)
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